A bold attempt by Theresa May to crack the Brexit impasse ran into trouble on Thursday as the Irish prime minister warned a new customs plan signed off by her warring ministers could be insufficient to avoid a hard border.

The prime minister has persuaded reluctant Brexiters to agree to a plan to continue applying EU tariffs beyond the end of 2020, if no agreement has been reached to alleviate the need for border checks.

May is now expected to deliver formal proposals within a couple of weeks, following a frantic day of diplomacy in the margins of an EU security conference that took her to Bulgaria and Macedonia.

She sought to rally support from EU leaders for a new plan for the so-called “backstop”, which would kick in if no solution has been found to the challenge of avoiding a hard border.

Q&A

What is a customs union and why does it matter?

A customs union is an agreement by a group of countries, such as the EU, to all apply the same tariffs on imported goods from the rest of the world and, typically, eliminate them entirely for trade within the group. By doing this, they can help avoid the need for costly and time-consuming customs checks during trade between members of the union. Asian shipping containers arriving at Felixstowe or Rotterdam, for example, need only pass through customs once before their contents head to markets all over Europe. Lorries passing between Dover and Calais avoid delay entirely.

Customs are not the only checks that count – imports are also scrutinised for conformity with trading standards regulations and security and immigration purposes – but they do play an important role in determining how much friction there is at the border. A strict customs regime at Dover or between Northern Ireland and the Republic of Ireland would lead to delays that will be costly for business and disruptive for travellers. Just-in-time supply chains in industries such as car making could suffer. An Irish peace process built around the principle of entirely unfettered travel between north and south could be jeopardised.

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After a 45-minute bilateral, the taoiseach, Leo Varadkar, reported that he had seen “new thinking”. He said that he welcomed anything that would align all of the EU and the UK in terms of customs into the future. Brussels has made it clear that Ireland must be satisfied before any deal is accepted.

But he suggested checks would still be required at the border if the UK left the single market.

He said: “Any move on customs with the UK would be welcome but I need to be very clear that avoiding a hard border between Northern Ireland and Ireland is about more than customs. The single market and aspects related to regulation are important as well.”

On Thursday, May – with her chief Brexit adviser Olly Robbins – had a series of meetings with the German chancellor Angela Merkel and the French president Emanuel Macron, and further meetings with the EU commission president Jean-Claude Juncker and the European council president Donald Tusk, as well as Varadkar.

At a press conference in Skopje, Macedonia, at the end of the day, May confirmed she still intended to seek a UK-wide proposal that would avoid the need for the backstop to be invoked, and would take Britain out of the customs union.

“We will be, in future, outside that customs union able to develop our own independent trade policy,” she said.

It would mean as frictionless trade as possible, she insisted.

But while her statement reiterated familiar pledges, it was also compatible with the latest proposal.

At a press conference before boarding the plane to return to London, the prime minister said: “In December, when the joint report was published between the European Union and the United Kingdom, we set out clearly options in relation to the commitment that we have given for no hard border between Northern Ireland and Ireland.

“We expect that to be dealt with through the overall relationship we have with the European Union. But there were then two further levels of option, including the final fallback option.

“The commission then published a fallback option which was not acceptable to to us. And we will be bringing forward our own proposal for that fallback option in due course.”

EU sources said the prime minister was firmly told by Tusk, during a meeting that she personally requested, that Brussels and Dublin needed to see the concept on paper before they could give May any confidence about the June European council summit.

The prime minister was said to appear anxious to know whether the proposal could lead to Brussels starting work on a political declaration about the future trading relationship with the UK.

Varadkar had warned earlier at the summit in Sofia that, without substantial progress on the question of the Irish border, “we need to seriously question whether we’re going to have a withdrawal agreement at all”.

The EU official said the meeting with Tusk had been about the UK’s “expectations in June”.

He said: “We had to say it was too early to tell. All the news coming from London is very disorientating. Tusk was clear that it is not only about what the commission might recommend.

“They have to get all 27 member states to agree, and that includes Ireland. And Tusk is squarely behind Dublin.”

Where do the Brexit negotiations stand?

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Varadkar later told reporters that, during 45 minutes of talks, May had sketched out her hopes for what he described as a “deep customs arrangement”, a phrase which will likely inflame Brexiters in the UK, who fear that their hopes of independent trade policy post-Brexit could be scotched.

Varadkar said: “The prime minister gave me an insight into some new thinking that the UK government has in relation to customs, and obviously we’ll see how that develops, we haven’t seen any detail of that yet.

“But certainly I think any move on customs which brings the UK closer to the EU is to be welcomed, but I very much emphasised that resolving the issue of a hard border requires more than customs.”